Ge∕Si islands in a three-dimensional island crystal studied by x-ray diffraction

Coplanar high-resolution x-ray diffraction has been used for the characterization of size, chemical composition, and strain of Ge∕Si (001) islands in a three-dimensional island crystal grown using self-assembly on a prepatterned (001) Si substrate. The measured diffusely scattered intensity is simulated using the kinematical approximation and the parameters of model islands are fitted. These simulations require calculations of the strain fields within the islands and the spacer layers. For this purpose, an analytical approach to solve the continuum elasticity equations has been extended to a full three-dimensional calculation. The Ge content in the islands is found to be on the average 40%, and the island shape does not change dramatically during capping.